[Paper Review] Evaluation of disconnected contributions using GPUs

Constantia Alexandrou, Vincent Drach+5 more|arXiv (Cornell University)|Nov 1, 2012

Particle physics theoretical and experimental studies5 references4 citations

TL;DR

This paper presents a GPU-accelerated computation of disconnected quark contractions for nucleon observables using the Truncated Solver Method (TSM) and the one-end trick with Nf=2+1+1 twisted mass fermions. The method enables precise estimation of nucleon form factors, σ-term, and axial charge by combining low-precision stochastic inversions with high-precision corrections, achieving reliable results at scale on modern GPU hardware.

ABSTRACT

We calculate on GPUs the disconnected diagrams associated with the nucleon form factors and moments of generalized parton distributions using Nf=2+1+1 twisted mass fermions. We employ the truncated solver method (TSM) for estimating the all-to-all propagators. Due to the fact that the TSM involves many low precision stochastic estimators, the usage of GPUs is essential to perform efficiently the contractions and the inversions.

Motivation & Objective

• To compute disconnected contributions to nucleon observables such as the σ-term and axial charge, which are critical for reducing systematic errors in lattice QCD.
• To overcome the high computational cost and gauge noise inherent in disconnected diagrams through algorithmic improvements and GPU acceleration.
• To validate the reliability of the Truncated Solver Method (TSM) combined with the one-end trick for variance reduction in disconnected contractions.
• To demonstrate the feasibility of computing disconnected diagrams for flavor-singlet quantities using modern GPU architectures.

Proposed method

• Employing the Truncated Solver Method (TSM) to reduce computational cost by using low-precision (LP) stochastic inversions and correcting for bias via high-precision (HP) inversions.
• Using N=24 high-precision sources and N=300 low-precision sources per configuration to balance accuracy and performance, tuned empirically to minimize error at lowest cost.
• Applying the one-end trick with twisted mass fermions to reduce variance in isoscalar matrix elements by exploiting symmetry properties of the fermion action.
• Combining TSM with the plateau and summation methods to suppress excited-state contamination and improve signal-to-noise ratios in time-correlation functions.
• Utilizing GPU-accelerated solvers to efficiently perform the large number of low-precision inversions required by TSM, enabling scalable computation.
• Performing stochastic estimation via random Z2/Z4 sources, with the estimator converging as O(1/√N), and correcting for bias in the TSM framework.

Experimental results

Research questions

• RQ1 Can the Truncated Solver Method (TSM) be effectively applied to disconnected contractions in lattice QCD with Nf=2+1+1 twisted mass fermions?
• RQ2 Does GPU acceleration enable a practical and scalable solution for the high computational cost of disconnected diagrams?
• RQ3 To what extent does the one-end trick reduce variance in isoscalar disconnected matrix elements without increasing computational cost?
• RQ4 How do the plateau and summation methods compare in suppressing excited-state contamination in nucleon observables?
• RQ5 Can reliable results for the nucleon σ-term and axial charge be obtained using TSM with GPU-accelerated stochastic estimation?

Key findings

• The TSM with 24 high-precision and 300 low-precision sources achieved the lowest computational cost while saturating to the gauge noise level for the tested diagram.
• The summation method successfully suppressed excited-state contributions, yielding a linear dependence on sink-source separation with a stable slope, consistent with plateau results.
• The generalized one-end trick produced noisier results than the standard version, but still enabled reliable extraction of the isoscalar gA from disconnected contractions.
• The results for the charm content of the nucleon (Fig. 2) and the σ-term of the Δ (Fig. 3) showed good agreement between plateau and summation methods, validating the approach.
• The light σ-term of the Ω baryon (Fig. 4) showed a strong signal with high statistical significance, even with limited statistics (4643 configurations).
• The isoscalar axial charge gA^is computed using the generalized one-end trick showed agreement with recent Clover fermion results, confirming consistency and reliability of the method.